Resumen

Cuando se calcula porcentajes para recuenios en diversas categorías o para varias medidas positivas, tomando cada una como una fracción de su. suma, a menudo, los porcentajes redondeados no suman 100 porciento. I nvestigamos la frecuencia con que ocurre este error y cuales son las distribuciones de las sumas de los porcentajes redondeados, para (1) un conjunto de datos empiricos; (2) la distribución polinomial en muestras pequeñas; (3) espaciamientos entre puntos ubicados en un intervalo, el modelo de la barra quebrada; y (4) para la simulación de varias categorias. Los diversos métodos producen distribuciones similares.

Hallamos que en promedio, la probabilidad de que la suma de los porcentajes redondeados alcance exactamente a 100 porciento, es evidente para dos categorias; es cerca de tree cuortos para tres categorías; cerca de dos tercios para cuatro categorías; y cerca de para un mayor número de categorías c, cuando las categorias no son improbables.

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Summary

When percentages are computed for counts in several categories or for several positive measurements0 each taken as a fraction of their sum, the rounded percentages often fail to add to 100 percent. We investigate how frequently this failure occurs and what the distributions of sums of rounded percentages are for (1) an empirical set of data, (2) the multinomial distribution in small samples, (3) spacings between points dropped on an interval—the broken-stick model—; and (4) for simulation for several categories. The several methods produce similar distributions.

We find that the probability that the sum of rounded percentages adds to exactly 100 percent is certain for two categories, about three-fourths for three categories, about two-thirds for four categories, and about for larger numbers of categories, c, on the average when categories are not improbable.

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